NAIROBI, Kenya (AP) — Ethiopian Prime Minister Abiy Ahmed again ruled out dialogue with the leaders of the defiant Tigray region Friday but said he was willing to speak to representatives "operating legally” there during his meeting with three African Union special envoys trying to end the deadly conflict between federal troops and the region's forces.

The meeting came as more people fled Tigray’s capital city ahead of a promised “final phase” of the army’s offensive. Meanwhile, the number of people managing to cross the border into Sudan has slowed to a trickle, raising concerns they are being blocked from leaving.

The Nobel Peace Prize-winning prime minister, who has resisted international mediation as “interference,” said he appreciated the AU envoys’ “elderly concern” but told them his government’s failure to enforce the rule of law in Tigray would “nurture a culture of impunity with devastating cost to the survival of the country,” according to his office. Abiy’s government and the regional one run by the Tigray People’s Liberation Front each consider the other illegitimate.

There was no immediate word from the three AU envoys, former Liberian President Ellen Johnson Sirleaf, former Mozambique President Joaquim Chissano and former South African President Kgalema Motlanthe. AU spokeswoman Ebba Kalondo did not say whether they can meet with TPLF leaders, something Abiy's office has rejected.

“Not possible,” senior Ethiopian official Redwan Hussein said in a message to the AP. “Above all, TPLF leadership is still at large.” He called reports that the TPLF had appointed an envoy to discuss an immediate cease-fire with the international community “masquerading.”

Fighting reportedly remained well outside the Tigray capital of Mekele, a densely populated city of a half-million people who have been warned by the Ethiopian government that they will be shown “no mercy” if they don't distance themselves from the region's leaders.

Tigray has been almost entirely cut off from the outside world since Nov. 4, when Abiy announced a military offensive in response to a TPLF attack on a military base. That makes it difficult to verify claims about the fighting, but humanitarians have said at least hundreds of people have been killed.

The fighting threatens to destabilize Ethiopia, which has been described as the linchpin of the strategic Horn of Africa.

With transport links cut, food and other supplies are running out in Tigray, home to 6 million people, and the United Nations has asked for immediate and unimpeded access for aid.

Multiple crises are growing. More than 40,000 refugees have fled for Sudan, where people struggle to give them food, shelter and care. One humanitarian agency says hospitals in Tigray are running out of drugs. And fighting near camps of Eritrean refugees in northern Ethiopia has put them in the line of fire.

Worryingly, refugees in Sudan have told The Associated Press that Ethiopian forces near the border are impeding people from leaving. Reporters from the AP have seen that crossings have slowed to a trickle in recent days. Ethiopia’s government has not commented on that.

Nearly half of the refugees are children. The spread of COVID-19 is just one concern.

“We cannot keep social distancing here in the camp,” said Mohammed Rafik Nasri, from the U.N. refugee agency. “It is really challenging among the several issues in need that are growing because the number is growing. Today we are receiving a convoy of 1,000 arriving in the camp. And shelter is one of the biggest challenges that we have at the moment.”

Scared, sometimes without word of loved ones left behind, the refugees continue to share horrific accounts of the fighting.

“The country has no peace. You see one tribe killing another. It is so hard,” said one, Atsbaha Gtsadik.

Meanwhile, some of the tens of thousands of refugees from Eritrea who are living in northern Ethiopia have been in the line of fire as fighting sweeps by them.

“Reports of conflicts around refugee camps are very concerning,” said Juliette Stevenson, a spokeswoman with the U.N. refugee agency. Communications and transport restrictions make it impossible to verify camp conditions, she said.

But the 96,000 Eritrean refugees “will run out of food as soon as Monday if supplies cannot reach them,” the agency said in a statement.

The International Committee for the Red Cross, in a rare dispatch from inside Tigray, warned that health care facilities are running out of drugs and other supplies and health workers need help caring for the wounded.

While traveling in western Tigray, the ICRC found a number of displaced people living in a makeshift camp without food, water or medical care. “They told us they feared for their lives, and that they wanted safe passage out of the area.”

Its statement added: “So much is still unknown on the level of violence and subsequent suffering that people in the Tigray region have endured in just three weeks."

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Associated Press journalist Fay Abuelgasim in Umm Rakouba, Sudan, contributed to this report.